In the climate sciences, parametrization schemes have been traditionally formulated in such a way that one expresses the net impact on the scales of interest of processes occurring within the unresolved scales via deterministic functions of the resolved variables, as in the pioneering work on the parametrization of convective processes by Arakawa and Schubert [1]}. More recently, it has been recognized, mostly on empirical grounds, that parametrizations should involve stochastic and non-Markovian components [2]}, [3]}, [4]}. Machine learning methods have been proposed as the next frontier of data-driven parametrizations [5]}, [6]}, [7]}, able to deliver a new generation of Earth system models [8]}; see, though, the caveats discussed by [9]}.
